Scientific Computing

This module demonstrates the Levenberg-Marquardt method for nonlinear least squares. Given an approximate solution, a new approximate solution is computed as a weighted combination of the Gauss-Newton step and the steepest descent direction. This process is repeated until convergence.

The user selects a problem either by choosing a preset example or
typing in a desired function *f* of parameters
*x*, *y*. Contours of the least squares residual are drawn
on the plot. An initial guess *x*, *y*)*x*, *y*)*μ* can be selected by the user using the slider provided. The
approximate solution is updated using the computed step, and the
process is then repeated. If the starting guess is close enough to the
true minimum, then the Levenberg-Marquardt method usually converges to
it, typically with a linear convergence rate.

**Reference:** Michael T. Heath, *Scientific Computing,
An Introductory Survey*, 2nd edition, McGraw-Hill, New York,
2002. See Section 6.6.2 and Example 6.15.

**Developers:** Jeffrey Naisbitt and Michael Heath